Work

Tropical friezes and cluster-additive functions via Fock-Goncharov duality and a conjecture of Ringel

Year: 2026

Type: article

Abstract: We study tropical friezes and cluster-additive functions associated to symmetrizable generalized Cartan matrices in the framework of Fock-Goncharov duality in cluster algebras. In particular, we generalize and prove a conjecture of C. M. Ringel on cluster-additive functions associated to arbitrary Cartan matrices of finite type. For a Fock-Goncharov dual pair of positive spaces of finite type, we use tropical friezes and cluster-additive functions to explicitly express the Fock-Goncharov pairing between their tropical points and the bijections between global monomials on one and tropical points of the other.

Source: Forum of Mathematics Sigma

DOI: 10.1017/fms.2026.10291

Authors: Peigen Cao, Antoine de Saint Germain, Jiang-Hua Lu

Institutions: University of Science and Technology of China, University of Hong Kong

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,650

Funders: National Natural Science Foundation of China, Japan Society for the Promotion of Science, Basic and Applied Basic Research Foundation of Guangdong Province